There is no good way to describe what the MWI says happens to your experience using ordinary language. The problem is that words like "you" and "experience" can't possibly mean in the MWI what they mean in ordinary conversation. In the case you describe, there will be a "you" that experiences A and a "you" that experiences B, and both of these "yous" will be "descended", physically, from "you" before the measurement. But are they "the same" you, having both experiences? There is no good answer, because the underlying assumptions behind our ordinary concept of "the same" are not valid for this case.